4. 1 Apply Congruence and Triangles 4

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Presentation transcript:

4. 1 Apply Congruence and Triangles 4 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: To define congruent triangles To write a congruent statement To prove triangles congruent by SSS, SAS

Congruent Polygons

Congruent Triangles (CPCTC) Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent.

Congruence Statement When naming two congruent triangles, order is very important.

Example Which polygon is congruent to ABCDE? ABCDE  -?-

Properties of Congruent Triangles

Example What is the relationship between C and F?

Third Angle Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Congruent Triangles Checking to see if 3 pairs of corresponding sides are congruent and then to see if 3 pairs of corresponding angles are congruent makes a total of SIX pairs of things, which is a lot! Surely there’s a shorter way!

Congruence Shortcuts? Will one pair of congruent sides be sufficient? One pair of angles?

Congruence Shortcuts? Will two congruent parts be sufficient?

Congruent Shortcuts? Will three congruent parts be sufficient? And if so….what three parts?

Investigation… … Using 2,3,4 Triangles

Side-Side-Side Congruence Postulate SSS Congruence Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

SSS Congruence Postulate

Using a 2-Column Proof! Is ABC is congruent to ABD? Why or why not?

Example Decide whether the triangles are congruent. Explain your reasoning.

Investigation… … Part 2

Congruence Shortcuts Side-Angle-Side (SAS) Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Can we prove?...yet?

What else would we need?

Can we Prove Triangle Congruence?

Another Proof…?

Classwork From 4.1 3 - 12 32 – 35 38 – 40 46 – 48* From 4.2 1 - 4 8 - 17 22 - 30 41 - 42